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Study sets matching "conics"

19 terms
Conics
What is the Directrix ?
What is the Focus of a parabola?
Equation of Parabola in Standard Form
Equation of Parabola in Vertex Form
A fixed line that defines the parabola. Every point on the pa…
What is the Directrix ?
A fixed line that defines the parabola. Every point on the pa…
What is the Focus of a parabola?
18 terms
Conics
Center of a Circle
Circle
Conic Section
Diameter
The point inside the circle that is the same distance from al…
The set of all points in a plane that are the same distance,…
A figure formed by the intersection of a plane and a right ci…
The distance across a circle through its center. The line seg…
Center of a Circle
The point inside the circle that is the same distance from al…
Circle
The set of all points in a plane that are the same distance,…
16 terms
Conics
Circle
Standard Form of a Circle
Center of a Circle
Radius of a Circle
The set of all points that are equidistant from a point calle…
(x - h)2 + (y - k)2 = R2
(h , k)
R
Circle
The set of all points that are equidistant from a point calle…
Standard Form of a Circle
(x - h)2 + (y - k)2 = R2
9 terms
Conics
unit circle
derivative of parametric equation
parametric equation
equations of an ellipse
unit circle
derivative of parametric equation
19 terms
Conics
What is the Directrix ?
What is the Focus of a parabola?
Equation of Parabola in Standard Form
Equation of Parabola in Vertex Form
A fixed line that defines the parabola. Every point on the pa…
What is the Directrix ?
A fixed line that defines the parabola. Every point on the pa…
What is the Focus of a parabola?
26 terms
Conics
Equation of horizontal ellipse
Equation of vertical ellipse
Foci of horizontal ellipse
Directrices of horizontal ellipse
(+- C, 0)
x=a^2/c
Equation of horizontal ellipse
Equation of vertical ellipse
15 terms
Conics
distance formula
midpoint formula
standard form for a circle
domain and range of a circle
used to find diameter or radius when given 2 sets of points
used to find the center
x^2 + y^2 = r^2 OR (x-h)^2 + (y-k)^2 = r^2... x and y coefficie…
[brackets], domain - left to right, range - bottom to top
distance formula
used to find diameter or radius when given 2 sets of points
midpoint formula
used to find the center
17 terms
conics
parabola is when...
parabola x^2... parabola y^2
parabola vertical equation
parabola horizontal equation
either x or y is squared
vertical... horizontal
y-k = a(x-h)^2
x-h = a(y-k)^2
parabola is when...
either x or y is squared
parabola x^2... parabola y^2
vertical... horizontal
19 terms
Conics
Axis
Branch
Center
Circle
The line over which a parabola is symmetric.
The term for each of the two distinct sections of the graph o…
For an ellipse and hyperbola, the midpoint between the foci.…
The set of all points equidistant from a given fixed point.
Axis
The line over which a parabola is symmetric.
Branch
The term for each of the two distinct sections of the graph o…
31 terms
Conics
Circle
Standard Form of a Circle
Center of a Circle
Radius of a Circle
The set of all points that are equidistant from a point calle…
(x - h)2 + (y - k)2 = R2
(h , k)
R
Circle
The set of all points that are equidistant from a point calle…
Standard Form of a Circle
(x - h)2 + (y - k)2 = R2
24 terms
Conics
Form of an Equation:... y = a(x-h)^2 + k…
Form of an Equation:... x = a(y-k)^2 + h…
Vertex
Axis of Symmetry
Up if a > 0, down if a < 0
Right if a > 0, Left if a < 0
Always (h,k)
x=h in up/down parabola & y=k in right/left parabola
Form of an Equation:... y = a(x-h)^2 + k…
Up if a > 0, down if a < 0
Form of an Equation:... x = a(y-k)^2 + h…
Right if a > 0, Left if a < 0
26 terms
Conics
Equation of horizontal ellipse
Equation of vertical ellipse
Foci of horizontal ellipse
Directrices of horizontal ellipse
(+- C, 0)
x=a^2/c
Equation of horizontal ellipse
Equation of vertical ellipse
19 terms
Conics
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1
Ellipse (left to right)
Ellipse (up and down)
Hyperbola (left and right sides)
Hyperbola ( top and bottom)
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
Ellipse (left to right)
(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1
Ellipse (up and down)
33 terms
Conics
Circle
radius
Standard form of a circle
Center of circle
the set of all points in a plane that are equidistant from a…
the distance from the center to any point on the circle
(x-h)^2+(y-k)^2=r^2... or ... x^2+y^2=r^2
(h,k)
Circle
the set of all points in a plane that are equidistant from a…
radius
the distance from the center to any point on the circle
9 terms
Conics
Parabola
Circle
Ellipse
Hyperbola
Only one squared term
Same coefficient, same sign
Different coefficient, same sign
Different signs
Parabola
Only one squared term
Circle
Same coefficient, same sign
Conics
ellipse horizontal
ellipse vertical
circle
to find c of an ellipse
c2 = a2 - b2
ellipse horizontal
ellipse vertical
10 terms
Conics
Circle
Ellipse
Parabola: y =
Parabola: x =
Circle
Ellipse
9 terms
Conics
ellipse horizontal
ellipse vertical
circle
to find c of an ellipse
c2 = a2 - b2
ellipse horizontal
ellipse vertical
17 terms
conics
parabola is when...
parabola x^2... parabola y^2
parabola vertical equation
parabola horizontal equation
either x or y is squared
vertical... horizontal
y-k = a(x-h)^2
x-h = a(y-k)^2
parabola is when...
either x or y is squared
parabola x^2... parabola y^2
vertical... horizontal
16 terms
Conics
Circle formula at origin
Circle formula if not at origin
Radius formula
Parabola formula at origin and horizon…
x²+y²=r²
(x-h)²+(y-k)²=r²
√x²+y² & r²=x²+y² & r=√(x₂-x₁)+(y₂-y₁)
y²=±4px
Circle formula at origin
x²+y²=r²
Circle formula if not at origin
(x-h)²+(y-k)²=r²
11 terms
Conics
distance formula
midpoint formula
ellipse formula
hyperbola formula
distance formula
midpoint formula
11 terms
Conics
Circle Formula
Midpoint formula
Distance formula
pythagorean theorem
(x-h)²+(y-k)²=r²
{(x₁+x²)/2, (y₁+y₂)/2)}
√(x₁-x₂)²+(y₁-y₂)²
a²+b²=c²
Circle Formula
(x-h)²+(y-k)²=r²
Midpoint formula
{(x₁+x²)/2, (y₁+y₂)/2)}
23 terms
Conics
x²+y²+4x−8y=0
x²-y²+4x-8y=0
2x²+2y²+4x-8y=0
2x²-2y²+4-8y=0
Circle
Hyperbola
Circle
Hyperbola
x²+y²+4x−8y=0
Circle
x²-y²+4x-8y=0
Hyperbola
33 terms
CONICS
how know if equation is a circle
how know if equation is a parabola
how know if equation is an elipse
how know if equation is a hyperbola
2 squared terms
1 squared term
2 squared terms = 1
2 squared terms and (-) sign
how know if equation is a circle
2 squared terms
how know if equation is a parabola
1 squared term
51 terms
CONICS
m = tanA
tanA = (m2-m1)/(1+m2m1)
equal
It satisfies the equation
The angle of inclination
The angle of intersection between two lines
Vertical angles are...
If a point is on a conic, ...
m = tanA
The angle of inclination
tanA = (m2-m1)/(1+m2m1)
The angle of intersection between two lines
14 terms
Conics
circle
midpoint formula
distance formula
parabola equation
(helps graph circles)
(helps graph circles)
opens up or down: (x-h)² =(+/-) 4p(y-k)... opens right or left:…
circle
midpoint formula
(helps graph circles)
31 terms
conics
vertical form for parabolas
focus for vertical form of a parabola
directrix vertical form of a parabola
to classify a conic what part of the e…
x2= 4py
(0, p)
y= -p
Ax2 + Bxy +Cy2
vertical form for parabolas
x2= 4py
focus for vertical form of a parabola
(0, p)
34 terms
Conics
Parabola
Point F
Line l
Vertex V
The set of points in the plane equidistant from the focus and…
Focus
Directrix
Lies halfway between the focus and the directrix
Parabola
The set of points in the plane equidistant from the focus and…
Point F
Focus
43 terms
Conics
The definition of a conic
The number of conics
Who invented the conics
The names of the conics
Graphs that are created by slicing a cone
4
Ancient Greeks
Parabola, circle, ellipse, hyperbola
The definition of a conic
Graphs that are created by slicing a cone
The number of conics
4
26 terms
Conics
circle
parabola
ellipse
hyperbola
coefficients same, both squared
only one variable squared
coefficients different, both squared & positive/negative
only one squared is negative
circle
coefficients same, both squared
parabola
only one variable squared
19 terms
Conics
x^2=4py
y^2=4px
to find the equation of the tangent li…
in an ellipse, a is always the
opens left/right, parabola
opens up/down, parabola
distance formula with the focus point and the point on the pa…
longest/major axis
x^2=4py
opens left/right, parabola
y^2=4px
opens up/down, parabola
14 terms
Conics
Parabola
Parabola directrix
Parabola Foci
Circle
x^2,y x^2=4py
y=-p
(0,p)
(x-h)^2+(y-k)^2=r^2
Parabola
x^2,y x^2=4py
Parabola directrix
y=-p
49 terms
Conics
Parabola
Vertex form for a vertical parabola
What is the direction of a vertical pa…
What is the direction of a vertical pa…
The set of points equidistant from a fixed point and a fixed…
y = a(x-h)^2 + k
Upwards
Downwards
Parabola
The set of points equidistant from a fixed point and a fixed…
Vertex form for a vertical parabola
y = a(x-h)^2 + k
24 terms
Conics
Circle general equation
Circle standard equation
Parabola opening upwards gen equation
Parabola opening downwards gen equation
(x-h) ² +(y-k) ² =r ²
x ² +y ² +Dx+Ey+F=0
(x-h)² =4p(y-k)
(x-h)² = -4p(y-k)
Circle general equation
(x-h) ² +(y-k) ² =r ²
Circle standard equation
x ² +y ² +Dx+Ey+F=0
8 terms
Conics
Form of equation (y)
Form of equation (x)
Axis Of Symmetry for Y=
Axis Of Symmetry for X=
y= a(x-h)^2+k
x= a(y-k)^2+h
x=H
y=K
Form of equation (y)
y= a(x-h)^2+k
Form of equation (x)
x= a(y-k)^2+h
15 terms
Conics
A=C
A doesnt = C but a, c are positive
A, C= 0 (only 1 Squared term)
A or C is negative
Circle
Ellipse
Parabola
Hyperbola
A=C
Circle
A doesnt = C but a, c are positive
Ellipse
12 terms
Conics
Circle
Circle
Parabola (Vertically aligned)
Parabola (Horizontally aligned)
(X-h)^2 +(y-k)^2=r^2
Center= (h,k)
(x-h)^2=4p(y-k) // ^
(y-k)^2=4p(x-h) // ><
Circle
(X-h)^2 +(y-k)^2=r^2
Circle
Center= (h,k)
19 terms
Conics
distance
circle (y=)
circle (r=)
ellipse pythagorean relationship
d=√(x₂-x₁)²+(y₂-y₁)²
y=±√r²-(x-h)² +k
r=√(x-h)²+(y-k)²
a²=b²+c²
distance
d=√(x₂-x₁)²+(y₂-y₁)²
circle (y=)
y=±√r²-(x-h)² +k
31 terms
conics
ellipse identity
hyperbola identity
parabola identity
circle identity
diff #, same sign
opp signs
a=0 OR c=0
a=c
ellipse identity
diff #, same sign
hyperbola identity
opp signs
31 terms
Conics
Each conic is governed by a
Sum of the distances from the foci is…
Differences of the distances from foci…
The set of all points in a plane that…
Locus
Ellipse
Hyperbola
Parabola
Each conic is governed by a
Locus
Sum of the distances from the foci is…
Ellipse
16 terms
conics
distance formula
midpoint formula
normal parabola
sideways parabola
square root of [(X2-X1)^2 +(Y2-Y1)^2]
(X1+X2)/2, (Y1+Y2)/2
x^2=4py
y^2=4px
distance formula
square root of [(X2-X1)^2 +(Y2-Y1)^2]
midpoint formula
(X1+X2)/2, (Y1+Y2)/2
20 terms
Conics
Circle (rect)
Circle (polar)
Parabola (rect)
Parabola (polar)
A=C
e= 0
AC= 0
e= 1
Circle (rect)
A=C
Circle (polar)
e= 0
15 terms
Conics
(x-h)^2+(y-k)^2=r^2
(x-h)^2=4p(y-k)
(y-k)^2=4p(x-h)
P
Standard form of a circle
Standard form of a vertical parabola
Standard form of a horizontal parabola
Represents the distance between vertex and focus for a parabola
(x-h)^2+(y-k)^2=r^2
Standard form of a circle
(x-h)^2=4p(y-k)
Standard form of a vertical parabola
9 terms
Conics
standard equation of circle
midpoint formula
standard equation of vertical parabola
standard equation of horizontal parabola
r²=(x-h)²+(y-k)²
(x₁+x₂/2, y₁+y₂/2)
(x-h)²=4p(y-k)
(y-k)²=4p(x-h)
standard equation of circle
r²=(x-h)²+(y-k)²
midpoint formula
(x₁+x₂/2, y₁+y₂/2)
21 terms
Conics
conic
circle
parabola
ellipse
ax² + by² + cx + dy + e = 0... a and b ≠ 0
ax² + by² + cx + dy + e = 0... a = b
ax² + by² + cx + dy + e = 0... either a = 0 or b = 0
ax² + by² + cx + dy + e = 0... a and b are positive and a ≠ b
conic
ax² + by² + cx + dy + e = 0... a and b ≠ 0
circle
ax² + by² + cx + dy + e = 0... a = b
19 terms
Conics
parabola
P
directrix
focus
the set of all points that are equidistant from the focus and…
the distance from the vertex to the focus
a line that is a distance of P from the vertex in the opposit…
a point inside the parabola that is a distance of P from the…
parabola
the set of all points that are equidistant from the focus and…
P
the distance from the vertex to the focus
8 terms
Conics
hyperbola equation
hyperbola asymptotes
hyperbola foci
ellipse equation
(x^2/a^2)-(y^2/b^2)=1... (y^2/b^2)-(x^2/a^2)=1
+-(b/a)x
(a+b)^1/2
(x^2/a^2)+(y^2/b^2)=1... (y^2/b^2)+(x^2/a^2)=1
hyperbola equation
(x^2/a^2)-(y^2/b^2)=1... (y^2/b^2)-(x^2/a^2)=1
hyperbola asymptotes
+-(b/a)x
31 terms
Conics
Up or down
Parabola
Parabola
Parabola opening up
If X is first in a parabola it opens
Includes Latus Rectum which includes focus point
Distance from focus to vertex is length a
(X-2)^2=8(y-1)
Up or down
If X is first in a parabola it opens
Parabola
Includes Latus Rectum which includes focus point
9 terms
Conics
Parabolas (horizontal, open side to si…
Parabolas (vertical, open up and down)
Ellipse (horizontally long)
Ellipse (vertically long)
(y-k)^2 = 4p(x-h)
(x-h)^2 = 4p(y-k)
(x-h)^2 / a^2 + (y-k)^2 / b^2 =1
(x-h)^2 / b^2 + (y-k)^2 / a^2 =1
Parabolas (horizontal, open side to si…
(y-k)^2 = 4p(x-h)
Parabolas (vertical, open up and down)
(x-h)^2 = 4p(y-k)
16 terms
Conics
Parabola Equation
Ellipse Equation
Hyperbola Equation
Parabola Vertex
(x-h)2 = 4p(y-k)
(x-h)2/a2+(y-k)2/b2=1
(x-h)2/a2-(y-k)2/b2=1
(h , k)
Parabola Equation
(x-h)2 = 4p(y-k)
Ellipse Equation
(x-h)2/a2+(y-k)2/b2=1
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